# How do you solve k^2=76?

Jul 4, 2017

See a solution process below:

#### Explanation:

First, take the square root of each side of the equation to solve for $k$ while keeping the equation balanced. Remember, the square root of a number produces both a positive and negative result.

$\sqrt{{k}^{2}} = \pm \sqrt{76}$

$k = \pm \sqrt{76}$

We can now simplify this using this rule for radicals:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$k = \pm \sqrt{\textcolor{red}{4} \times \textcolor{b l u e}{19}}$

$k = \pm \sqrt{\textcolor{red}{4}} \times \sqrt{\textcolor{b l u e}{19}}$

$k = \pm 2 \times \sqrt{\textcolor{b l u e}{19}}$

$k = \pm 2 \sqrt{\textcolor{b l u e}{19}}$

If necessary: $\sqrt{19} = 4.359$ rounded to the nearest thousandth

$k = \pm 2 \cdot 4.359$

$k = \pm 8.718$ rounded to the nearest thousandth